Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received April 30, 2014; final manuscript received April 26, 2015; published online June 8, 2015. Assoc. Editor: Zhongquan Charlie Zheng.

Abstract

Protein aggregation, one of the common molecular mechanisms for neurodegenerative diseases, is affected by variety of physical factors, one of which is shear rate of protein solution. This paper provides theoretical background on the shear rate in the experimental system we have proposed to effectively apply and control shear. We carried out the mathematical analysis of the flow field resulted from torsional or transverse oscillation on the outer boundary between two concentric hemispheres by perturbation method. We have obtained analytical solutions for the velocity field, the shear rate, and the flow pattern of steady streaming created by the nonlinear interaction of the oscillatory flow.

Figures

First-order dimensionless shear stress profiles on the equatorial plane over one time period for the torsional oscillation in a sphere. The dashed curve shows the time-average of absolute shear stress values over one period: (a) α = 1, (b) α = 5, and (c) α = 20.

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